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---
layout: page
lang: en
header: "Ternary logic and ternary computers"
---
<div class="row">
<div class="col-sm-6 col-md-7 col-lg-8">
<p>
The ternary symmetric number system is a positional integer numeral system with a base of 3 and values of -1, 0, +1 (the symbols used are: +, 0, -). It is the <a href="/kb/04b1e68c-7add-426d-bed3-a0dab0ec452d">most efficient</a> among the integer positional systems.
</p>
<p>
The key feature of the ternary symmetric system is the inclusion of the sign of the number in the alphabet itself:
</p><ul class="marked">
<li>the sign of the number is clearly defined by the number itself;</li>
<li>ease of performing arithmetic operations;</li>
<li>rounding off numbers is easily achieved by simply discarding the less significant digits.</li>
</ul>
(See <a href="/kb/3d3703c1-75fb-4bf8-9041-a27d34a30508">Ternary arithmetic</a>)
<p></p>
<p>The <a href="/kb/5267fd6d-6395-49ec-a9b7-e10709c83995">use of ternary code and three-valued logic in computers</a> has an undeniable advantage over binary systems, which was demonstrated by the operation of the ternary computer Setun. The efficiency of ternary logic in programming languages was implemented in DSSP.
</p>
</div>
<div class="col-sm-6 col-md-5 col-lg-4">
<section class="tr-sidebar-section">
<h3 class="tr-sidebar-section-header">
<a href="/projects/translator">Ternary Base Converter</a>
</h3>
<div class="machine-translator translator-lite" data-behavior="trinary-translator">
<div class="input-group">
<label class="input-group-addon translator-label" for="number_bin" title="Двоичная">Bin</label><input class="input-sm form-control" data-kind="binary" id="number_bin" placeholder="0 1" type="text">
</div>
<div class="input-group">
<label class="input-group-addon translator-label" for="number_tri" title="Троичная">Tri</label><input class="input-sm form-control" data-kind="trinary" id="number_tri" placeholder="- 0 +" type="text">
</div>
<div class="input-group">
<label class="input-group-addon translator-label" for="number_oct" title="Восьмеричная">Oct</label><input class="input-sm form-control" data-kind="octonary" id="number_oct" placeholder="0 1 2 3 4 5 6 7" type="text">
</div>
<div class="input-group">
<label class="input-group-addon translator-label" for="number_non" title="Девятеричная">Non</label><input class="input-sm form-control" data-kind="nonary" id="number_non" placeholder="w x y z 0 1 2 3 4" type="text">
</div>
<div class="input-group">
<label class="input-group-addon translator-label" for="number_dec" title="Десятичная">Dec</label><input class="input-sm form-control" data-kind="decimal" id="number_dec" placeholder="0 1 2 3 4 5 6 7 8 9" type="text">
</div>
<div class="input-group">
<label class="input-group-addon translator-label" for="number_hex" title="Шестнадцатеричная">Hex</label><input class="input-sm form-control" data-kind="hexadecimal" id="number_hex" placeholder="0 1 2 3 4 5 6 7 8 9 a b c d e f" type="text">
</div>
</div>
</section>
<section class="tr-sidebar-section" id="trinary-clock-sinchron-section">
<h3 class="tr-sidebar-section-header">
<a href="/projects/sinchron">Ternary clock "Sinchron"</a>
</h3>
<a href="/projects/sinchron/fullscreen"><canvas id="trinary-clock-sinchron-canvas" width="300" height="150"></canvas></a>
<script type="text/javascript">
//<![CDATA[
$(document).ready(function(){
var section = document.getElementById('trinary-clock-sinchron-section');
var placeholder = document.getElementById('trinary-clock-sinchron-canvas');
var tc = new trinary.clock.Sinchron(placeholder, section.clientWidth, 150);
tc.sinus.hour.amplitude = 0.97;
tc.sinus.minute.amplitude = 0.65;
tc.sinus.second.amplitude = 0.35;
tc.sinus.millisecond.amplitude = 0.1;
tc.canvas();
});
//]]>
</script>
</section>
<section class="tr-sidebar-section">
<h3 class="tr-sidebar-section-header">
<a href="/projects/calendar">Ternary calendar</a>
</h3>
<div id="calendar_container"></div>
<script type="text/javascript">
//<![CDATA[
$(window).ready(function(){
var calendarium = new trinary.calendar.Calendarium();
var today = new Date();
var monthCalendar = calendarium.renderMonth(today.getFullYear(), today.getMonth() + 1, [today.getDate()]);
$('#calendar_container').html(calendarium.wrap(monthCalendar));
})
</script>
</section>
</div>
</div>